IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-0-387-68361-4_5.html
   My bibliography  Save this book chapter

Sparse Sets in Time and Frequency Related to Diophantine Problems and Integrable Systems

In: Additive Number Theory

Author

Listed:
  • D. V. Chudnovsky

    (Polytechnic Institute of NYU, IMAS)

  • G. V. Chudnovsky

    (Polytechnic Institute of NYU, IMAS)

  • T. Morgan

    (Polytechnic Institute of NYU, IMAS)

Abstract

Summary Reconstruction of signals and their Fourier transforms lead to the theory of prolate functions, developed by Slepian and Pollack. We look at prior contributions by Szegö to these problems. We present a unified framework for solutions of Szegö like problems for signals supported by an arbitrary union of intervals, using the techniques of Garnier isomonodromy equations. New classes of completely integrable equations and Darboux–Backlund transformations that arise from this framework are similar to the problems encountered in transcendental number theory. A particular example for the Hilbert matrix is studied in detail.

Suggested Citation

  • D. V. Chudnovsky & G. V. Chudnovsky & T. Morgan, 2010. "Sparse Sets in Time and Frequency Related to Diophantine Problems and Integrable Systems," Springer Books, in: David Chudnovsky & Gregory Chudnovsky (ed.), Additive Number Theory, edition 1, pages 77-98, Springer.
    • Handle: RePEc:spr:sprchp:978-0-387-68361-4_5
    DOI: 10.1007/978-0-387-68361-4_5
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sprchp:978-0-387-68361-4_5. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.